CREEP Of SMALL WOOD BEAMS UNDER CONSTANT PENDING LOAD

RICULTURE ROOM

CREEP Of SMALL WOOD BEAMS UNDER

CONSTANT PENDING LOAD

September 1939

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UNITED STATES DEPARTMENT OF AGRICULTURE

FOREST SERVICE

Pe taxon with the University of Wisconsin

FOREST PRODUCTS LABORATORY

MADISON 5, WISCONSIN

CREEP OF SMALL WOOD BEAMS

UNDER CONSTANT BENDING LOAD)"

By

WILLIAM S. CLOUSER, Engineer

Forest Products Laboratory,? Forest ServiceU. S. Department of Agriculture

INV I. IMIS

Summary

An analysis of creep occurring in small Douglas-fir beams tested at midspanunder concentrated loads ranging from 6o to 95 percent of ultimate is pre-sented. The experiments were performed under conditions of constant temper-ature and relative humidity that maintained the specimens at 6 or 12 percentequilibrium moisture content for periods as long as 10 years. A power lawequation, e = eo + atm, is used to describe the creep curve up to the pointof inflection. Results are presented in terms of stress level, power lawequation constants, creep rate, and time.

Introduction

A series of experiments was begun at the Forest Products Laboratory in 1943to determine the behavior of small, clear, simply supported Douglas-fir beamsin controlled atmospheres under three types of load applied at midspan.

The types of loading employed were: (1) Constant dead loads of predeter-mined size applied until failure of the beam occurred; (2) loads applied bydropping shot into a box hung from the beam at a constant rate so as tocause failure in a predetermined time; and (3) repeated load cycles tofailure in which the beams were alternately subjected to dead loads for aweek and then allowed to recover for a week after removal of the loads.

In this report are presented the results obtained in series of tests per-formed with constant loads applied until failure of the specimen took place.The behavior of the specimens is analyzed with respect to such factors asamount of deflection, rate of deflection, and life of the specimen for dif-ferent atmospheric conditions.'

The increasing deflection of a loaded beam with the passage of time is com-monly called creep. Under proper conditions, creep is common to all mate-rials, and it has long been recognized as an important consideration in thedesign of timber structures that must have a long life, often under heavy

-"This report is based upon a thesis for a Ph.D. degree in mechanics at theUniversity of Wisconsin.

Maintained at Madison, Wis., in cooperation with the University of Wisconsin.

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loads. The results of creep may be observed in buildings in the form ofsagging joists and rafters or the more familiar example of sagging bookcasesand storage shelves.

Suprisingly little work has been done on this problem up to the present, thebulk of it in recent times. The decrease in breaking strength of a timberbeam under a continuing load has beep recognized at least since the begin-ning of the eighteenth century (1k).— Buffon (8) experimented with oak beamsin 1740 to determine a safe load for long-time loading. Tiemann as) re-ported that Herman Haupt made a series of tests to show the effect of pro-longed loading on various woods in 1841, and that Denton and Riesenbergertested long-leaf pine in bending in 1880. Other work, minor in scope, wasalso done.

Most of the work in the field of creep, however, has been done during thepresent century, possibly because of the emphasis on research during thepast two major wars and the diminution of natural resources in the morehighly developed parts of the world. A number of investigations have beencarried out, starting with Tiemann's work at Yale in 1907-09 (511). Somework was done in Germany in the 1930's. Vorreiter (60 summarized the workof K. Egner in 1934 on "pine," which included some loading periods as longas 700 days. Kollman (22) concisely related the work of Ph. Roth in 1935and the well-known work of O. Graf ( fl ). In this country, Draffin andMuhlenbruch ran bending tests on balsa with durations from 100 to 600 days(Lk)

In 1947, L. W. Wood reported on the first results of the Forest ProductsLaboratory experiments (61). In Australia, Kingston and Armstrong (2/028)reported work on initially green Tasmanian oak beams, which was followed in1953 by Armstrong's work with 12 small air-dried specimens (2). From 1956to 1958 Hideo Sugiyama of Meiji University, Tokyo, completed a series oftests on small beams of Japanese woods, most of which were for 3 months orless, but some of which extended to approximately a year (V1,10.

In all of the work reported, there was little if any control of atmosphericconditions. The difficulties involved in maintaining a closely controlledatmosphere are many, especially when this must be done for very long periodsof time. The work which comes closest to attaining this goal is the seriesof tests at Madison.

Details of these various experiments are to be found in the references cited.The tests indicated rough agreement on the following points:

(1) A load less than 45 to 60 percent of the short-time ultimate load (basedon the modulus of rupture) did not cause failure in the beams during thetime alloted to the experiments.

lUnderlined numbers in parantheses refer to literature cited at the end ofthis report.

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(2) An increase in moisture content during the test caused an increase inthe deflection of the beam although the load remained constant.

(3) The higher the moisture content of the wood at the start of the test,the greater was the total deflection at any given time.

The results of these tests, together with long experience in the behavior ofstructural timber, are reflected in the recommendations made for long-timeloading design stresses by various organizations.

The Forest Products Laboratory (20) recommends the use of a basic workingstress suitable for use in long-time loading under full load. A factor ofnine-sixteenths is used to convert the ultimate strength in the standardshort-time test to a corresponding strength under long-time loading. Otherfactors are then applied to arrive at the basic stress. This long-timestress value is then modified for short times, for example 10 years, byfactors obtained from an empirical curve derived by Wood (64).

In the "National Design Specifications for Stress-Grade Lumber and ItsFastenings" (40), a "normal loading" presumed safe for a cumulative 10-yearduration of load is used as a base. This figure can then be adjusted to fitthe duration expected.

The problem of the large deflection (which may be more than twice the ini-tial deflection without failure) is simply solved by halving the modulus ofelasticity in static bending or by setting the initial allowable deflectionat one-half the long-time allowable deflection (20).

Creep

As is well known, the static testing of materials is often not sufficientfor the determination of their behavior for present-day applications. Therate of application of the load and the time that the load remains in placeare extremely important factors. Consideration of these factors requiresthat information be obtained about behavior with respect to time as well asdata on short-time stresses and strains.

The responses of nearly all materials to loads of long duration are similar,although from the standpoint of mechanism the similarity may be more appar-ent than real.

If deformation (expressed as strain, elongation, or deflection) is plottedagainst time, a curve similar to that shown in figure 1 will result. Thecurve can be divided into four parts. The initial deformation, OA, is thatoccurring when the load is applied. It is, for all practical purposes,usually considered to be instantaneous and, depending upon the magnitude ofthe load, may be composed of elastic, delayed elastic, and plastic

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deformations. These, however, are developed in a relatively short time asthe load increases and are therefore considered together for constant loadtests.

The primary stage, AB, of the creep curve, also called the transient creepstage, describes a period during which the rate of deformation constantlydecreases. This decrease continues until the secondary stage, BC, isattained. The secondary stage, or steady-state part of creep, is usuallyconsidered the period of constant rate of deformation. Thus, BC is astraight line of minimum slope. This region is joined smoothly to a terti-ary stage, CD, in which the deformation rate increases and failure of thespecimen ultimately occurs.

In practice, the form of the curve may depart widely from that shown infigure 1. Figure 2 shows the forms usually taken as either the load or thetemperature is raised. The curves from A to D represent increasing tempera-ture or increasing load.

The slope of the curve may be dependent upon other factors, such as moisturecontent of the specimen, changing ambient conditions, and structural changesin the specimen. This is especially true in hydrophilic substances, suchas concrete, many plastics, and wood. Structural changes are important inmetals and in the aging of concrete and plastics. Rotherham ( IE) shows afew of the infinite variations that can occur in practice to influence theshape of the curve.

The steady-state region, BC, has been the subject of much study in the searchfor relations that would permit prediction of the time of failure of a givenspecimen from the results of short-time tests. Although the region is mostoften treated as a straight line, a question arises as to whether it is notactually a very flat reverse curve with a point of inflection, such as themore pronounced example D in figure 2, with a point of inflection E. Theproblem here is that the measurement of such small deformations is eitherimpossible with the gages at hand, or the magnitude of other factors in theexperimental setup effectively masks the small changes in deformation. Thestraight-line part often shrinks to a point as the temperature and load areincreased.

At low temperatures and low loads, the creep rate may appear to become zero.Although this is a value often cited in the literature as a limiting rate,it has not been shown that failure will not occur, merely that failure hasnot occurred. The limiting creep stress is a useful idea from an engineeringviewpoint, however, since a material which has a zero (or near zero) creeprate for "a very long time" can be extremely valuable.

The final portion of the curve shown in figure 1 has been investigated farless than have the other parts. Since a material which has entered thisstage has, for design purposes, failed, many tests are stopped when thisstage is reached in order to save time and money. A further deterrent withmetals has been the belief that failure in this stage was due to necking of

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the specimen. This belief arose as a result of the early work of Andrade(4) and others, who maintained that this stage was absent under constantstress loadings. From the experiments of Sully and others (1/), the exist-ence of this final stage in metals under constant stress is now recognized.

Creep of Metals

Extensive study has been given to determining the effect of external andmetallurgical factors upon creep of metals and the mathematical expressionsthat relate the observed creep variables. Creep is basically affected bythe applied stress, the composition of the specimen, and the size and numberof the crystals in the specimen.

Primary creep in metals is due largely to slip. The amount of slip dependsupon the stress and the temperature, and the slip rate decreases with time.Secondary creep is attributed primarily to grain boundary movements. Thesliding of the grain boundaries allows a substantial amount of deformation,which can be interpreted as viscous flow and treated as a rate process. Thethird stage is one of progressive internal fracture that develops directlyfrom the grain boundary deformations of the second stage.

Any or all of these processes (together with others not mentioned) may besimultaneous. In addition, the temperatures at which creep usually is im-portant in metals may induce significant changes in the structure and proper-ties of the metal, which can complicate the creep processes.

Comprehensive treatment of the creep of metals may be found in referencesCO, (LW) ( 1L), (a), (.a), and (50-

Creep of Concrete

Concrete is an intimate mixture of a hardened water-cement paste and a coarsematerial of varying composition and particle size, called the aggregate.Under long-time loading, concrete undergoes creep deformation, which in-creases at a decreasing rate while the load is acting. The heterogeneousnature of concrete and the colloidal nature of the cement paste allow manydeformation processes to occur during long-time loading, such as viscousflow of the water-cement paste, plastic flow in the crystalline aggregate,closure of voids, and flow of water from the cement gel and the capillariesin the mass as a result of external loads and drying. The changes in watercontent just mentioned depend not only upon the relative humidity of the ex-ternal atmosphere but also upon the moisture gradient within the capillaries.The amount of deformation that can be ascribed to each process is variablebecause of the many concrete mixtures that are made possible by changing thecomposition or the proportions of the ingredients.

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Since some of the deformation processes are dependent on time, such factorsas age before loading, treatment during aging and curing, the magnitude ofthe load, and the length of time that the load is applied contribute asmuch to the creep of concrete as the materials used in making it.

Some surveys of the creep of concrete give extensive bibliographies (12),(ii), (42), and (61).

Creep of Wood

Wood is a complex, anisotropic, porous, naturally expanded material. Thecomposition varies slightly from species to species, but the most importantconstituents common to all are cellulose, hemicellulose, and lignin. Cellu-lose and hemicellulose make up 70 to 80 percent of the weight of ovendrywood, and lignin 20 to 30 percent.

The cellulose molecule has hydroxyl (-OH) groups at regular intervals. Theseare responsible for the adsorption of water molecules and for bonding cellu-lose molecules to each other in the crystallites that form the minute struc-ture of the cell wall. Although the resulting individual bonds are weak,there are so many that the total binding energy is great enough to preventthe separation of the cellulose chains by water. This force also preventsthe melting of cellulose at high temperatures.

This exclusion of water from the interior of the crystallite leads to theadsorption of water only in the amorphous regions and on the surfaces of thecrystallites. In a humid atmosphere dry wood adsorbs moisture, the watermolecules becoming attached to the accessible hydroxyl groups. The attach-ment produces swelling of the wood, principally in the radial and tangentialdirections and to only a slight extent longitudinally, since the fibrils areapproximately parallel to the axis of the cell. This suggests for wood thesame possibility that has been presented for concrete (-L,46), that unequalshrinkage stresses may contribute to creep.

The presence of water facilitates plastic strain in wood by weakening bondsbetween some of the cellulose chains. An increase in temperature will weakenthe bonds by increasing thermal molecular movement.

If applied strains are not large enough to break bonds, the wood will behaveelastically. If the strains do break bonds, there will be differentialmovement between the chains with exchange of bonds and inelastic strain.Permanent strain can also occur upon rupture of molecules or by shearing ofthe crystallites. These processes would be more likely to occur in the finalstages of creep or at a very high creep rate.

In the light of the structure and chemistry of wood, these assumptions aboutcreep mechanisms are valid. It must be remembered, however, that wood is anatural product and, as such, has a host of growth features such as knots,pitch pockets, and grain irregularities, that introduce an empirical factorinto the description of the creep process.

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Excellent summaries exist on high polymers and their properties (18, 112)The structure of wood and cellulose and the changes occurring with moisturechanges are to be found in (6,2208).

The Mathematical Description of Creep

Mathematical expressions to describe creep range from simple relationshipsthat fit experimental data to complex relationships based on assumptionsregarding the creep mechanism.

In the following discussion, a few of the more widely used treatments areoutlined. The chief variables involved are either creep and time, or creep,stress, and time.

The fact that the creep curve is apparently linear in the secondary stage ledMcVetty (5.2) to formulate an expression as follows:

Assume an asymptotic approach to the minimum creep rate (the slope of theportion BC in figure 1); then

de - Vo = Be-Kt

dt

where de is the rate of change of deformation, V o is the minimum Creep ratedt

(slope of BC), B and K are constants, and t is time.

Integrating

c = Eo + Vot - e -Kt

where c is the total deformation and eo the intercept of the straightline

part, on the deformation axis.

For large 14 this approaches the expression:

C = CO Vot

This equation has been extremely useful in the study of primary and secondarycreep. Of course, it is of no value beyond the straightline range and isnot accurate for the many materials that have no straightline part to theircreep curve. It is still used and forms the basis for many extremely compli-cated expressions (16).

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Weaver (62) assumed that the creep rate is inversely related to time andapproaches a constant value.

= Vo +dt

where , is a constant and the others as before. Then

= Vot + a • log t + a constant

For metals, these terms are interpreted as structural changes that modifyviscous flow.

The fact that many materials yield a straight line when the logarithm ofcreep is plotted against that of time has often been noted. The expressionobtained from this line is the power law. This empirical treatment is attri-buted to Sturm, Dumont, and Howell (22), although Filon and Jessop utilizedthis relation in 1923 (n). The plot leads to an equation:

log (c - co) = log b + m log t

where g , is total creep, eo is a constant derived from the data which includeselastic and plastic deformation, and b and m are constants.

This gives

= co + btm

This expression has been used to describe creep behavior in metals, plastics(11,1a,150,16,11012), and crystalline nonmetals (1).

In the field of concrete, similar empirical expressions have been employed.For example, Straub (51) used a generalized power law containing as variablesstress, deformation, and time.

= kaPtg

where g. is the unit plastic deformation after time,, . a coefficient obtainedfrom tests, sz the unit stress, and p. and g are constants depending upon theelastic properties at the beginning of the stressed condition.

Shank (5.,Q) proposed a modification based on the assumption that creep is pro-portional to the unit stress.

y = Ctl/a

where I is the plastic flow per unit stress, t is time, and C and a are con-stants determined for the particular concrete and the loading conditions.

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Lorman ( .11) used a hyperbolic form based on the work of Ross:

= mt an + t

where e is creep strain, m. a constant called the "creep coefficient," n acreep-time constant, t is time reckoned from when the load is applied, a isstress, and m and n are constants determined from the conditions of loading.

McHenry () related creep, time, and loading and aging factors in an expres-sion for the creep due to a unit load.

Q= au - e-rt) pe -pk (1 - e-mt)

where Q is creep strain due to unit load, a, r, nj and m are constantsevaluated from the experimental conditions, and k is age at time of loading.This equation is based on the superposition principle of Boltzmann (I)Leaderman (,32) and Gross (24) have given extensive treatments of this prin-ciple, which has had wide application in the primary creep of visco-elasticmaterials. Small strains, deformations which are linear functions of theload, and complete recovery of creep are basic assumptions in this theory,which states that the total deformation of a material with a history of vary-ing loads (removal of a load being considered a negative application of thesame load) is the sum of the deformations that would be produced from eachof the loads applied separately.

Several other representations that are appearing in the literature should bementioned. Although certain of them are claimed to have a basis in the funda-mental relations of the physics and chemistry of matter, the work involvingthem is as yet on a semiempirical basis and much remains to be done beforeany of them can be considered as nonempirical.

Nadal and McVetty (U) employed the empirical relation:

V = Vo Binh (c2...4

(ao)

where V is the minimum creep rate, a is the applied stress, and Vo and ao areexperimentally determined constants with dimensions of strain rate and stressrespectively. Although the occurrence of a hyperbolic sine function in ratetheory (21) has been considered to be an additional support for the Nadai ex-pression, Nadal apparently developed the relation originally as an empiricallybetter fit than the power law.

The rate process theory was originally applied to chemical reactions and tothe flow of liquids. It was extended to the case of solids by Kauzmann (aE)and many others, until a large literature now exists. Very briefly, theoverall process is the sum of numerous unit processes or units of flow.These units may be molecules for simple fluids, subgrains or dislocationsfor metals, and portions of chains in linear polymers. The units are assumed

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to be in thermal equilibrium and may only be moved to an adjacent positionby a shear force. This is accomplished by providing sufficient externalforce to overcome the potential energy barriers that keep the units in sta-tistical equilibrium. This, in turn, is assumed to be effected by loweringthe potential in the direction of action and raising it in the opposingdirection. The minimum energy supplied for movement is called the activa-tion energy. Perhaps the chief objections to the theory are the numerousparameters to be determined and the fact that it is applied principally tosecondary stage creep. Nevertheless, the activation energy approach doesattempt to tie together parameters obtainable from other types of experi-ments than creep.

Recently some "parameter" methods have been developed from the rate theorybackground in attempts to predict long-time strength from short-time tests.They all consist of some relation between the parameters of time or rate andtemperature and various experimentally determined constants. Two of thesimpler expressions are mentioned here:

Perhaps the simplest is the Larson-Miller parameter (3D) based on an equationdeveloped by Holloman and Jaffe for the tempering of steel:

K = T(C + log t)

where,, is a constant, I is the absolute temperature, and is the time torupture. C is usually taken as 20, but this is not necessarily a good prac-tice, since 20 is an average for many metallic alloys. The parameter hasbeen used for some work in plastics (aa).

The Manson and Haferd parameter (a) is based on experimental work ratherthan rate theory. It is of the form:

K= T

log t - log to

where Ta and to are temperature and time constants taken from constant stresstests a fairly short time.

In use, the logarithm of the initial stress is plotted against the parameterK for rupture times at high temperatures and extrapolated to lower tempera-tures.

A comparison of the various parameters dealing with metals is to be found inreference (24). Reference (2) has a comparison of several parameters used onglass-reinforced plastic laminates, With carefully worked examples. The pro-posed "Tentative Tests for Conducting Creep and Time-for-Rupture TensionTests of Materials" of the American Society for Testing Materials (2) statesin section 11 that these parameter methods must be employed with cautionuntil more data are obtained.

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Method of Test

The plan of the tests to be described was organized by G. W. Foster of theForest Products Laboratory in 1945. L. W. Wood, also of the Laboratory,modified the plan slightly and started the test series. The scope of thistest program is indicated in the Introduction. The following descriptionis limited to the experiments involving beams loaded to failure by constantload.

The beams to be tested were 1 by 1 by 22 inches in size and were cut fromflat-sawn, straight-grained, Douglas-fir planks 3 inches thick by 7 to9 inches wide selected from Laboratory stock. Each bending-test specimenwas flanked by two ring-matched control specimens. Figure 3 shows a few ofthe planks. The locations of the beams within the planks are marked by thepencilled squares on the ends of the pieces.

Table 1 shows the numbers of creep specimens and controls tested. From someplanks, five specimens were cut, the middle beam being used as a control forboth creep specimens.

Beams were brought to equilibrium with, and tested in, three atmospheric en-vironments: 75° F. and 64 percent relative humidity, 80° F. and 65 percentrelative humidity, and 80 0 F. and 30 percent relative humidity. In thefirst two, wood comes to an equilibrium moisture content of approximately12 percent, and in the last, approximately 6 percent.

During the tests, the specimens were loaded on a tangential face; that is,with the growth rings horizontal. Forty-eight controls were loaded at atesting machine head speed of 0.084 inch per minute. One hundred seventy-five were tested at a constant loading rate of 1 pound per second by drop-ping lead shot through a calibrated orifice into a box suspended at the mid-point of the specimen.

A deflection rate at the center of the beam of 0.084 inch per minute over an18-inch span is equivalent to the 0.10 inch per minute specified in ASTMSpecification D 143-52 (3). This is based on an outer fiber strain rate of0.0015 inch per inch per minute. The 1-pound-per-second loading rate givesa slightly lower strain rate, but within the 25 percent allowed. The75-pound-per-minute rate is nearly equivalent to the standard rate.

The moduli of rupture were computed for the controls, and the average modulusof rupture of the two controls for each creep specimen was assumed to be themodulus of rupture of the creep specimen. The load corresponding to a pre-determined percentage of this average modulus of rupture was computed andthen applied to the creep specimen.

Figure 4 shows four beams under test. The load was hung from the centerof each beam by means of an iron stirrup that terminated at its lower end ina wood platform upon which steel or lead bars and lead shot bags were placed.


The bars and bags were gently applied at an approximate rate of 75 poundsper minute. Care was taken to minimize impact loading caused by too rapidapplication of the weights. The loads placed on the beams were approxi-mately equal to the calculated load, but no attempt was made to equal thecalculated loads precisely. The load levels in table 1 are therefore purelynominal. A few of the higher level loads were applied with the apparatusused to load the controls. A protective framework was placed around each,test stand to prevent accidental jarring of the creep specimens.

The beams were simply supported on knife edges and rollers on 18-inch centers,and deflections were measured with a dial indicator reading to 0.001 inch.The bar supporting the dial indicator and the strap at the center of thebeam were pinned with small brads at the neutral axis. The dial indicatorwas attached to the center strap with fine wire and lightly preloaded, sothat all possible play was eliminated from the indicator linkages.

The control test data consisted of load and deflection measurements fromthe start of loading to failure, together with observations on the behaviorof the specimen.

Deflection at the center and the time of reading comprised the bulk of thecreep-test data. Careful records were taken of changes in the conditioningof the rooms in which the specimens were kept, and the behavior of the beamswas closely watched. Observations were taken at intervals of a minute orless during loading and at less frequent intervals as the deflection ratedecreased with time. For the more extended tests (lower load levels), read-ings were taken once a day or even once a week.

An attempt was made at all times to record the progress of the failure ofthe beams. For short-time tests at high loads no problems were encountered,but the failure of the beams tested with small loads was more difficult topredict. Consequently, times recorded for failures that occurred on theweekend or at night could be somewhat in error. If a failure was expected,an automatic recorder was employed that consisted of a rubber tube con-nected to a clockwork-driven pressure recorder. When a beam failed, theplatform holding the weight dropped on the tube and compressed it. Theresulting increase in pressure was recorded on the chart.

Mathematical Treatment of Data

The experimental data for the constant load series of tests consisted ofload-deflection data for the controls, the load, and the deflection-timedata for the test specimens, together with the record of the ambient con-ditions. during the tests. The time of failure was obtained directlywith an automatic recorder or, in the case of unexpected failure, could beestimated reasonably well.

The average of the moduli of rupture of the two controls for each creepspecimen was calculated and considered to be the modulus of rupture of the


creep specimen. The beams were rejected if the moduli of rupture of thecontrols were not nearly the same. As noted later, this value is notnecessarily correct, because of the defects inherent in wood. It was de-cided that the simple average of the controls was perhaps just as accurateas more elaborate weighting methods. Variations in growth structurewould influence the result as inexorably with any type of average. Therehas been little or no work published on this aspect of the determinationof properties.

A predetermined percentage of the load calculated for the average modulusof rupture was placed on the creep specimen. Since the weight placedon the beam only approximated the calculated weight, the percentage ofthe average modulus of rupture for the actual load was then calculated.This value is used in all subsequent data manipulations and referred to asthe "percentage of the average modulus of rupture" or, more simply, as the"stress level."

The influence of temperature and humidity on a loaded beam is shown in fig-ure 5. A phenomenon frequently observed is the "tension failure." This isnot always a visual phenomenon; often it is merely a distinctly audiblecrack accompanied by a perceptible increase in the beam deflection. Creeprate will often be very great immediately after the tension failure, butmay, in a reasonably short time, decrease to the creep rate prior to thefailure. Sometimes the crack will be accompanied by visible separation offine fibers from the tension side of the beam. It is suggested that thisis not a true tension failure, with destruction of the area under tension,but an internal readjustment which does nothing to disturb seriously thecross section of the beam.

The result of a large rise in temperature, or an increase in relative humid-ity, is an increase in the deflection. The immediate effect of temperaturechange on most static strength properties of dry wood is to decrease or in-crease the property 1/3 to 1/2 percent for each 1 0 rise or drop in tempera-ture in the neighborhood of 70° F. Correspondingly, the change in staticbending properties due to a change of 1 percent in moisture content isroughly 4 to 5 percent. The deflection behavior accompanying humiditychanges can be at least partially attributed to the weakening influenceof increases in moisture content on the outer fibers. The return of theatmosphere to normal is followed by gradual drying of the wood, and often aresumption of the original creep rate. If the creep rate returns to whatit was before the disturbance, the amount of the increase is subtractedfrom each ordinate in order to provide sufficient points for describing thecurve.

Since this was the first attempt to analyze all of the constant load data,all specimens were graphed. Deflection-time plots were prepared and allremarks made by observers noted on the graphs. The initial deflection andzero time were taken at the end of loading, since up to that time the loadhad been increasing. Smooth curves were drawn through the points except at


obvious discontinuities. The number of observations was, in most cases,more than sufficient to allow a curve to be drawn which accurately describedthe behavior of the specimen.

Consideration of the overall shape of the curves that generally had a pri-mary stage, a point of inflection rather than a well-defined straightlinesecondary stage, and a wide variety of shapes after the point of inflection,led (after a few trials) to the use of the empirical power law formula fora description of the behavior of the creep specimens before the point ofinflection was reached. The description of the curve after the point ofinflection is probably not possible until more is known about the manner inwhich the beams fail under long-time loading.

Since a smooth curve had been easily drawn through the points, the curvewas used for the calculation of the power law constants. The method usedwas an adaptation of one proposed by La Combe (12):

Let the form of the curve be

= co + atm

Where E and t are variable and c o , a, and m are constants; let the t's bechosen so that they form a geometric progression with the ratio r. Then theterms are

t1, t2 = tlr 1 t3 tlr2 to = tlrn - 1

For two consecutive values of 14

en + 1 = co

en = co

or

atE+1

atW

- tE) = atE(rm - 1)n + 1 - En = a(t1313-1

taking logarithms

log10 ie = log10 a(rm - 1) + m logiotn

a straight line in the variables logioLe and logiotn with slope m and inter-cept log10 a(rm - 1).

In summary, the required constants may be found by the following procedure.Choose a set of is in geometric progression with a ratio r, and tabulatethem with their corresponding c i s obtained from the curve. A series ofvalues of log10t and logic& will be found which will fall nearly on a


straight line. For such a few points it is a simple matter to obtain theslope constant, m, and the intercept constant, log10 a(rm - 1), by least

squares and from this obtain the slope constant, a. Knowing these a seriesof Eo t s can be calculated from the e's and t's that were originally chosen.

The average of these is the constant fa, which is used in the equation

= o atm

In order to have all data homogeneous in time, the is are all expressed inminutes by writing (6o t)m for t in hours and (1,440 t)m for t in days.

The various constants obtained from the equations were divided by the ini-tial deflection due to loading, 5 0 . This procedure removed some of thevariation due to specimen individuality.

Figures 6 through 11 are plots of the various parameters, Esc), a X 1,000,r VO

and m against stress level. Figures 12 through 17 are plots of stress levelsagainst the deflection at the point of inflection 5PIA ) the time at theP opoint of inflection, and the minimum creep rate.

The point of inflection and the minimum creep rate were determined graphi-cally. The trend lines were computed by the method of averages (48).

The trend lines for both equilibrium moisture contents are given on eachgraph for comparison purposes. The plotted points refer only to the solidline curve in each case.

Analysis of Data

Many factors can lead to difficulties in obtaining satisfactory data increep experiments. The estimation of a modulus of rupture for the creepspecimens destroys the compactness of the data by permitting unknown varia-tions due to defects, hidden in the structure of the specimen. Therefore,the actual short-time ultimate strength for the creep specimen is neverknown.

Figures 18 and 19 show the distribution of the stress levels with respectto times of failure under equilibrium moisture contents of 6 and 12 percent,respectively. The plots have the failing of all graphs with logarithmicaxes--that of "pushing together" the values so that a range of 1 day at oneend of the axis may occupy the same space as 2 or 3 years at the other end.Superposition of the figures shows much the same distribution of points forboth, regardless of the 6 percent difference in moisture content. Thetrend lines indicate that there is little difference to time of failure atequilibrium moisture contents of 6 and 12 percent. The 10 specimens condi-tioned at 80° F. and 65 percent relative humidity appear to be randomly


scattered through the 75° F. and 64 percent relative humidity specimens, andthere is no evidence that a 5° difference in conditioning temperature af-fected their life.

The equations for the trend lines are:

S.L. = 89 - 6 log TF ....(6 percent moisture content)

S.L. = 90 - 6 log TF ....(12 percent moisture content)

where S.L. is the stress level and T, the time to failure after loading, inhours.

Figures 14 and 15 are plots of the stress level against the time to the pointof inflection. This is a valuable point to be able to predict, since it ishere that failure can be said to begin. Superposition of the graphs showsthe points of the 6 percent plot falling among those of the 12 percent plotin a random manner. The points representing tests conducted at 80° F. and65 percent relative humidity appear to be well scattered among those repre-senting tests at 75° F. and 64 percent relative humidity. The 5° tempera-ture difference apparently has little effect. The equations for the trendlines are:

S.L. 88 - 6 log TF1 ....(6 percent moisture content)

S.L. = 91 - 7 log TF1 ....(12 percent moisture content)

where S.L. is the stress level and T the time at point of inflection._El

The lines intersect at roughly the 70 percent stress level. This intersec-tion possibly has little meaning, since, in addition to the natural spreadin the data, the point of inflection is difficult to locate accurately.The differences should probably be ignored and, within the range of 6 to 12percent, moisture content may be considered to have little effect on time topoint of inflection.

In figures 16 and 17, stress level is plotted against the minimum creep rate.This is the creep rate occurring at the time of the point of inflection.The equations for these figures are:

S.L. = 59 + 6 log 41in ...(6 percent moisture content)

S.L. = 56 + 7 log Emin ..•(12 percent moisture content)

Although these lines intersect, they do so at an even smaller angle thanthose in figures 14 and 15. The error involved in measuring the tangent tothe curve may be large, and it is surprising that the data are not more


erratic. On this basis, it appears reasonable to neglect the crossing ofthe lines and assume that there were only small differences in minimum creeprates between specimens at the two moisture contents.

The deflection at the point of inflection expressed in terms of initial de-flection, 50 , plotted against stress level is shown in figures 12 and 13.

The points for the 6 and 12 percent moisture content levels fall into dis-tinctly separate areas, in contrast to the plotted data previously shown.At any stress level, the ratio for the specimens at 12 percent moisture con-tent was approximately 1.21 times the ratio for those at 6 percent moisturecontent. The equations of the trend lines are:

S.L. 196 - 92 ( 8PI/50 ) ....(6 percent moisture content)

S.L. 222 - 93 ( 5PI/50 ) ....(12 percent moisture content)

The remaining graphs are concerned with the relations between the stresslevel and the various constants in the power law equation. Although theseconstants have no basis in physical reality, correlation with the conditionsof the experiment may be valuable for prediction purposes or for relatingother factors.

The three constants determine the shape and location of the curve. The con-stant, co , is similar to but not the same as the instantaneous deflectionin that it moves the intersection of the curve with the x-axis up or down.The constant, Do can be considered to be a magnification factor. The con-stant, p, provides information on the creep rate.

A plot of stress level and e /5 (figs. 6 and 7) indicates that e /5o o o o is almost independent of stress level. The 80° F. and 65 percent relativehumidity points are well scattered through the other 12 percent moisturecontent points. The near perpendicularity of the lines may be seen from theslopes of the equations, which are:

S.L..= 812 - 733 (e0/80 ) ...(6 percent moisture content)

S.L. = 66o - 586 (e/50 ) ...(12 percent moisture content)0

Figures 10 and 11 show the relations between m and the stress level. Therelationship for 6 percent moisture content is practically insensitive tostress level (within approximately 3 minutes of arc of being perpendicular),and has an average value of 0.35. The experimental errors and materialvariations could easily account for the slight deviation from the vertical.

The relationship for 12 percent moisture content is more difficult to ex-plain. Undoubtedly, much of the deviation of the line is due to the in-fluence of the points in the upper right-hand part of the graph. If these


were eliminated, the trend line would probably approach the vertical witha constant m value of about one-third. The small difference in roomtemperatures may have influenced the results, but this is impossible toshow from the data.

It is interesting to note that the value of the exponent, m $ has been foundto be nearly independent of stress (given the same material and temperatures)for iron, steel, several pure metals, and some reinforced plastics. Inaddition ) it has been found to be approximately equal to one-third forvarious materials, such as copper, lead, Ni-Cr-Mo steel, and concrete.

The equations for the lines are:

S.L. = -333 + 1,175 m (6 percent moisture content)

S.L. = 23 + 151 m (12 percent moisture content)

Figures 8 and 9 show the graph of stress level and log 151. X 1,0003. The

quantity increases for both moisture contents as the stress level increasesand is greater for the 12 percent-moisture content data. The 80° F. and65 percent relative humidity points are distributed evenly through the 75° F.and 64 percent relative humidity points.

The equations of the trend lines are:

= 49 + 22 log (a x 1,000) ...(6 percent moisture content)

(80

S.L. = 32 + 28 log X 1,000) ...(12 percent moisture content)so

For the various relations that have been considered above, the limits ofthe values for the specimens at 12 percent moisture content appear to be alittle wider in general than the limits for those at 6 percent. This canbe observed in the slightly larger scatter of the points in the 12 percentgraphs as opposed to the 6 percent graphs.

Part of the spread may be due to the greater difficulties that arose inthe operation of the air conditioner for the 12 percent equilibrium moisturecontent room during the course of these experiments. A wide spread charac-terizes the data of these experiments in particular and of wood in general.Much of it is due to the natural variation found in clear wood specimens,but many serious defects also develop during growth, and these are hiddenuntil the wood is tested. The method of determining the stress level fromthe controls may provide more inaccuracies, which increase the scatter ofthe data.


Conclusions

The following conclusions are based on the reported test conditions andtest data:

1. The creep behavior up to the point of inflection can be satisfactorilydescribed by an empirical expression of the form, e = co +atm. The con-

stant, m, has a value of about one-third and is probably independent ofstress level and moisture content within the range studied. The constant( a X 1,000), should increase with an increase in stress level or moistureb"-

content.

2. The time to failure will increase as the stress level is decreased andis independent of moisture content for the levels used in these experiments.

3. The time to the point of inflection of the creep curve can be used topredict the start of failure of the beam. This time is dependent uponstress level and independent of the moisture content at the levels employedin these tests.

4. Since all specimens that were tested failed, the creep limit, if itexists, must be below the 6o percent stress level.

5. Increasing the moisture content level from approximately 6 percent toapproximately 12 percent appears to increase the ratio of deflection forany given stress level by a factor of approximately 1.2.

6. Any effects arising from small temperature differences cannot be esti-mated from the data obtained.

7. The results of these tests and similar tests can be of value to theengineer and the designer in estimating the behavior of structures underlong-time loading.


Literature Cited

1. American Society for Metals.1957. Creep and Recovery, Cleveland: American Society for Metals,

372 pp.

2. American Society for Testing Materials.1958. Report of the Joint ASTM-ASME Committee on the Effect of

Temperature on the Properties of Metals, pp. 23-24.

3. American Society for Testing Materials.1955. Standard Method for Testing Small Clear Specimens of Timber.

1955 Book of ASTM Standards, Part 4. Specification D143 -52.

4. Andrade, E. N. da C.1914. The Flow in Metals Under Large Constant Stresses. Proceedings

of the Royal Society, Vol. 90, p. 329.

5. Armstrong, L. D.1953. Short Term Creep Tests on Air-Dry Wooden Beams. Division of

Forest Products (Sub. Proj. T.P. 16-1), Australian CSIRO.Progress Report No. 2, September.

6. Barkas, W. W.1949. The Swelling of Wood Under Stress. Department of Scientific and

Industrial Research, Forest Products Research, London. 103 pp.

7. Boltzmann, L.1876. Zur Theorie der Elastischen Nachwirkung. Pogg. Ann. Physik,

Vol. 7, p. 624.

8. Buffon, G. L. L. De.1740. Experiences sur la Force du Bois. Paris L'Academie Royale des

Sciences. Histoire et Memoires, Vol. 292. Also Vol. 453(1741).

9. Carey, R. H., and Oskin, E. T.1956. The Prediction of Long-Time Stress-Rupture Data From Short-

Time Tests. SPE Journal, Vol. 12, No. 3, p. 21.

10. Cottrell, A. H.1953. Dislocations and Plastic Flow in Crystals. Oxford University

Press, London. 223 pp.

11. Crussard, C.1946. Le Role des Joints Intergranulaires dans la Deformation des

Metaux. Application au Fluage et a la Fatigue. Revue deMetallurgie, Vol. 43, p. 307.


12. Davis, E. A.1943. The Creep and Relaxation of Oxygen-Free Copper. Journal of

Applied Mechanics. Vol. 10, p. A-101.

13. de La Combe, M. J.1939. Un Mode de Representation des Courbes de Fluage. Revue de

Metallurgie, Vol. 36, pp. 178-188.

14. Draffin, J. 0., and Muhlenbruch, C. W.1937. The Mechanical Properties of Balsa Wood. Proc., American So-

ciety for Testing Materials, Vol. 37, Pt. II, pp. 582-587.

15. Filon, L. N. G., and Jessop, H. T.1923. On the Stress-Optical Effect in Transparent Solids Strained

Beyond the Elastic Limit. Philosophical Trans. of the RoyalSociety of London. Ser. A., Vol. 223, pp. 89-125.

16. Findley, W. N.1944. Creep Characteristics of Plastics. American Society for Test-

ing Materials, Symposium in Plastics. p. 118.

17. Findley, W. N., and Khosla, G.1956. An Equation for Tension Creep of Three Unfilled Thermoplastics.

SPE Journal, Vol. 12, No. 12, p. 20.

18. Flory, P. J.1953. Principles of Polymer Chemistry. Cornell University Press,

Ithaca, N. Y. 672 pp.

19. Fluck, P. G., and Washa, G. W.1958. Creep of Plain and Reinforced Concrete. Journal of the Ameri-

can Concrete Institute, Vol. 29, No. 10.

20. U. S. Forest Products Laboratory.1955. Wood Handbook. U. S. Dept. of Agric. Agriculture Handbook

No. 72. 528 pp., illus.

21. Glasstone, S., Laidner, K. J., and Eyring, H.1941. The Theory of Rate Processes. McGraw-Hill, New York. 611 pp.

22. Goldfein, S.1954. Time-Temperature and Rupture Stresses in Reinforced Plastics.

Modern Plastics, Vol. 32, p. 148, December.

23. Graf, O.1938. Tragfghigkeit der BauhOlzer and der Holzverbindungen. Mitt.

Fachaussch. Holzfr., H. 20 S. 40. Berlin 1938 (Reported inReference 29, p. 866).


24. Gross, Bernhard.1953. Mathematical Structure of the Theories of Visco-Elasticity.

Hermann et Cie. Editeurs, Paris. 74 pp.

25. Heimerl„ S. S., and Haferd, A. M.1954. Time-Temperature Parameters and An Application to Rupture

and Creep of Aluminum Alloys. National Advisory Committeefor Aeronautics Technical Note 3195. June.

26. Kauzmann, W.1941. Flow of Metals From the Standpoint of the Chemical Rate

Theory. Trans. Amer. Institute of Min. and Met. Engr.,Vol. 143, pp. 57-81.

27. Kingston, R. S. T.1949. Creep in Initially Green Beams. Australian CSIRO, Division

of Forest Products, Exp. T.P. 16-1/1. Progress Report No. 1,June.

28. Kingston, R. S. T., and Armstrong, L. D.1951. Creep in Initially Green Wooden Beams. Australian Journal of

Applied Science, Vol. 2, p. 306.

29. Kollmann, Franz.1951. Technologie des Holzes and der Holzwerkstoffe. Erster Band,

Springer-Verlag, Berlin. 1,050 pp.

30. Larson, F. R., and Miller, J.1952. A Time-Temperature Relationship for Rupture and Creep Stresses.

Trans. American Society of Mechanical Engineers, Vol. 74,No. 5, PP. 765-775.

31. Lea, F. M., and Lee, C. R.1947. Shrinkage and Creep in Concrete. Proc., Symposium on the

Shrinkage and Cracking of Cementative Materials. Societyof Chemical Industry, London.

32. Leaderman, H.1943. Elastic and Creep Properties of Filamentous Materials and

Other High Polymers. The Textile Foundation, Washington.278 pp.

33. Lorman, W. R.1940. The Theory of Concrete Creep. Proc., American Society for

Testing Materials, Vol. 4o, pp. 1082-1102.

McHenry, Douglas.1943. A New Aspect of Creep in Concrete and Its Application to De-

sign. Proc., American Society for Testing Materials, Vol. 43,pp. 1069-1087.

34.


35. McVetty, P. G.1934. Working Stresses for High Temperature Service. Mechanical

Engineering, Vol. 56, pp. 149-154, March.

36. Manjoine, M. J., and Mudge, W. L.1954. Creep Properties of Annealed Unalloyed Zirconium. Proc.American Society for Testing Materials, Vol. 54, pp. 1050-1067.

37. Manson, S. S., and Haferd, A. M.1952. A Linear Time-Temperature Relation for Extrapolation of Creep

and Stress in Rupture Data. National Advisory Committee forAeronautics Technical Note 2890, March.

38. Merideth, R.1953. Mechanical Properties of Wood and Paper. Interscience Pub-

lishing Co., New York. 298 pp.

39. Nadal, A., and McVetty, P. G.1943. Hyperbolic Sine Chart for Estimating Working Stresses of

Alloys at Elevated Temperatures. Proc. American Society forTesting Materials, Vol. 43, pp. 735-748.

40. National Lumber Manufacturers Association.1953. National Design Specifications for Stress-Grade Lumber and

Its Fastening.

41. National Physical Laboratory.1956. Creep and Fracture of Metals at High Temperatures. National

Physical Laboratory, London. 419 pp.

42. Neville, A. M.1955. Theories of Creep in Concrete. ACI Journal, Vol. 27, NO. 1,

p. 47.

43. Ott, Emil.1943. Cellulose and Cellulose Derivatives. Interscience Publishing

Co., New York. 1176 pp.

44. Parent.1707. Experiences pour Connaitre la Resistance des Bois de Chene

et de Sapin. L'Academie Royale des Sciences, Paris.Historie et Memoires, 512.

45. Pickett, G.1942. The Effect of Change in Moisture-Content on the Creep of

Concrete Under a Sustained Load. ACI Journal, Proc., Vol.38,FP. 333-355.


46. Pickett, G.1946. Shrinkage Stresses in Concrete. ACI Journal, Proc., Vol. 1+2,

pp. 165-204, January; pp. 361-398, February.

47. Rotherham, L. A.1951. Creep of Metals. Institute of Physics, London. 80 pp.

48. Scarborough, J. B.1930. Numerical Mathematical Analysis. The Johns Hopkins Press,

Baltimore. 416 pp.

49. Schmidt, A. X., and Marlies, C. A.1948. Principles of High Polymer Theory and Practice. McGraw-Hill,

New York. 743 pp.

50. Shank, J. R.1935. The Mechanics of Plastic Flow of Concrete.

Vol. 32, pp. 149-180, November-December.

51. Smith, George.1950. Properties of Metals at High Temperatures.

New York. 401 pp.

ACI Journal, Proc.,

McGraw-Hill,

52. Straub, L. G.1931. Plastic Flow in Concrete Arches. Proc. American Society of

Chemical Engineers, Vol. 95, p. 613.

53. Sturm, R. G., Dumont, C. and Howell, F. M.1936. A Method of Analyzing Creep Data. Journal of Applied Mechan-

ics, Vol. 3, No. 2, pp. A62-A66.

Sugiyama, Hideo.1957. The Creep Deflection of Wood Subjected to Bending Under Con-

stant Loading. Trans., Architectural Inst. of Japan. No. 55,pp. 60-70, February.

55. Sugiyamal Hideo.1956. The Effect of Loading Time on the Bending Strength and Stiff-

ness of Wood. Trans., Architectural Inst. of Japan. No. 52,March. (Forest Products Laboratory Translation No. 324,March, 1957.)

56. Sully, A. H.1949. Metallic Creep. Butterworths Scientific Publications, London.

278 pp.

57. Sully, A. H., Cale, G. N., and Willoughby, G.1948. Nature, London, 162 / p. 411.


58. Tiemann, H. D.1909. Some Results of Dead Load Bending Tests of Timber by Means of

a Recording Deflectometer. Proc., American Society forTesting Materials, Vol. 9, pp. 534-548.

59. Tiemann, H. D.1951. Wood Technology. Pitman Publishing Co., New York. 396 pp.

60. Vorreiter, Leopold.1949. Holztechnologisches Handbuch. Verlag Georg Fromme and Co.,

Vienna. 548 pp.

61. Washa, George.1955. Volume Changes and Creep. Significance of Tests and Proper-

ties of Concrete and Concrete Aggregates. Spec. Tech. Pub.No. 169, American Society for Testing Materials.

62. Weaver, S. H.1936. The Creep Curves and Stability of Steels at Constant Stress

and Temperature. Trans., American Society of MechanicalEngineers, Vol. 58, p. 745.

63. Wood. L. W.1947. Behavior of Wood Under Continued Loading. Engr. News Record,

Vol. 139, No. 24, pp. 108-111.

64. Wood, L. W.1951. Relation of Strength of Wood to Duration of Load. Forest

Products Laboratory Report No. 1916, December.

Report No. 2150 -25- 1.-43

Table 1.-=The distribution of the bending tests of

the control and creep specimens

Stress.: Number of tests completed at--levell :- - _

75° F., 64 per- : 80° F., 65 per- : 80° F., 30 per-

: cent relative : cent relative : cent relative

: humidity : humidity humidity• :-- :-. : Creep : Control : Creep : Control : Creep : Control: specimen : specimen : specimen : specimen : specimen : specimen

Per- : : :

cent : : :

S :95 : 5 : lo . 9 18

•90 : 5 : lo : 4 : 8 8 : 16

85 : 6 : 12 : • • 9 18

8o : 5 : lo 2 : 4 : 9 18

75 : 6 : 12 • • 8 16

7o : 5 : lo 4 : 8 : 5 10

65 : 5 : to : . . 5 10

6o : 4 •. 8 . • 5 10

Totals : 41 : 82 10 : 20 : 58 116

1Stress level is the predetermined percentage of the average modulus ofrupture computed from the moduli of rupture of the two control beams.

Report No. 2150

Figure 3. --View of several flat-sawn Douglas-fir planks used in the creep tests. Theplanks were cut into 22-inch lengths, and the locations of the ring-matched controland creep specimens were marked in pencil on the ends of these lengths.

Z M 60881 F

Figure 4. --A typical test frame containing four creep specimens under constant load.The load was applied through an iron stirrup that terminated in. a wood platformholding the load of bars or bags of shot. The beams were simply supported on steelknife-edges and rollers. Deflections were shown directly on dial indicators. Notshown is the free-standing protective frame surrounding the stand.

Z M 80898 F

Documents

CREEP Of SMALL WOOD BEAMS UNDER CONSTANT PENDING LOAD